The present invention relates to a method of estimating a transmission channel. In other words, the invention proposes a method of estimating the impulse response of a transmission channel.
In a communications system, especially a radio communications system, a transmitter transmits a signal to a receiver via a transmission channel. The transmitted signal is subject to amplitude and phase fluctuations in the transmission channel, with the result that the signal received by the receiver is not identical to the transmitted signal. The signal fluctuations are essentially due to what the skilled person refers to as xe2x80x9cintersymbol interferencexe2x80x9d. This interference can result from the modulation law employed for transmission purposes, and it is also caused by multipath propagation in the channel.
It is found that the received signal is generally the result of a large number of reflections in the channel. The various paths taken by the transmitted signal lead to a variety of delays at the receiver. The impulse response of the channel represents all such fluctuations affecting the transmitted signal. It is therefore the fundamental characteristic representative of transmission between the transmitter and the receiver.
The impulse response of the channel is used in particular by an equalizer whose function is specifically to correct intersymbol interference at the receiver. A standard method of estimating the impulse response consists in placing a training sequence made up of known symbols in the transmitted signal. The sequence is chosen as a function of the modulation law and of the dispersion of the channel. In the present context, xe2x80x9cdispersionxe2x80x9d is to be understood as meaning the delay affecting a transmitted symbol taking the longest path of the channel relative to the same symbol taking the shortest path. The dispersion is routinely expressed as a multiple of the time between two successive transmitted symbols, i.e. a number of xe2x80x9csymbol periodsxe2x80x9d.
Two examples of prior art techniques for estimating the impulse response of a transmission channel will be mentioned.
The first technique uses particular training sequences referred to as constant amplitude zero autocorrelation (CAZAC) sequences. These sequences are described in an article by A. Milewski: xe2x80x9cPeriodic sequences with optimal properties for channel estimation and fast start-up equalizationxe2x80x9d, IBM Journal of Research and Development, Vol.27, No.5, September 1983, pages 426-431.
The GSM cellular mobile radio system uses training sequences TS made up of 26 symbols a0 to a25 taking the value +1 or xe2x88x921. These sequences have the following properties:                     ∑                  i          =          5                20            ⁢              a        i        2              =    16                      ∑                  i          =          5                20            ⁢                        a          i                ⁢                  a                      i            +            k                                =    0  
Letting d denote the dispersion of the channel, which takes the value 4 in the GSM, the estimate of the impulse response takes the form of a vector X with five components x0 to x4.
The received symbol sequence S corresponding to the training sequence TS is also made up of 26 symbols, denoted s0 to s25. The natural assumption is made here that the transmitter and the receiver are perfectly synchronized, in which case the estimate of the impulse response X is given by the following expression:       X    k    =            1      16        ⁢                  ∑                  i          =          5                20            ⁢                        a          i                ⁢                  s                      i            +            k                              
The CAZAC technique has the advantage that it is very simple to implement. However, it should be noted that each component of the impulse response is established from only 16 received symbols. Because the training sequence is made up of 26 symbols and the channel dispersion value is 4, there is information in the received signal that is not taken into account and this degrades performance compared to the theoretical ideal.
The second prior art technique uses the least squares criterion. It is described in particular in patent applications FR 2 696 604 and EP 0 564 849. It uses a measurement matrix A constructed from a training sequence TS of length n. The matrix has (nxe2x88x92d) rows and (d+1) columns, where d again represents the dispersion of the channel. The item in the ith row and the jth column is the (d+ixe2x88x92j)th symbol of the training sequence:   A  =      (                                        a            4                                                a            3                                                a            2                                                a            1                                                a            0                                                            a            5                                                a            4                                                a            3                                                a            2                                                a            1                                                            a            6                                                a            5                                                a            4                                                a            3                                                a            2                                                            a            7                                    …                          …                          …                          …                                      …                          …                          …                          …                          …                                      …                          …                          …                          …                          …                                                  a            25                                    …                          …                          …                                      a            21                                )  
The training sequence is chosen so that the matrix AtA, where the operator .t represents transposition, cannot be inverted. This is inherently the case for CAZAC sequences but is also the case for other sequences.
The first four symbols s0 through s3 in the sequence of received symbols are ignored because they also depend on unknown symbols transmitted before the training sequence, given that the value of the channel dispersion is 4. At the risk of using a misnomer, the received signal will therefore be defined as a vector S whose components are the received symbols s4, s5, s6, . . . , s25,
The estimate of the impulse response then takes the following form:
X=(AtA)xe2x88x921At.S
This least squares technique is slightly more complex than the preceding technique but it should be noted that the matrix (AtA)xe2x88x921At is calculated only once. Note also that each component of the estimate of the impulse response X is obtained from 22 received symbols, rather than from only 16 as in the CAZAC technique. Improved performance can therefore be expected.
Whatever technique is used, estimation errors are inevitable, however. Determining the impulse response is a problem that cannot be solved exactly in the presence of additive noise. Also, the prior art techniques implicitly assume that the impulse response can take any form.
Accordingly, an object of the present invention is to provide a method of estimating a transmission channel which has improved resistance to additive noise, in other words which leads to an error lower than the estimation error of prior art techniques.
According to the invention, the method of estimating a transmission channel requires a signal received by the channel and corresponding to a transmitted training sequence and includes the following steps:
acquiring a statistic of the transmission channel,
establishing an estimate of the impulse response of the channel weighted by said statistic of the channel by means of the received signal.
The statistic of the channel represents a value of the impulse response prior to acquisition of the received signal. Said weighting introduces the fact that the impulse response related to the received signal has a value which is probably closer to that prior value than a value very far away from it. Thus statistically, the estimation error is reduced.
The statistic advantageously corresponds to an estimate of the covariance of said impulse response.
A first variant of the method includes the following steps:
smoothing the impulse response and orthonormalizing by means of a transformation matrix W to obtain the estimate of the covariance which then takes the form of a matrix Lxe2x80x2,
seeking eigenvectors vixe2x80x2 and eigenvalues xcexixe2x80x2 associated with that matrix Lxe2x80x2,
estimating the instantaneous impulse response of the channel from the received signal and applying that transformation matrix W to form a vector Xxe2x80x2, so establishing the weighted estimate Xp:       X    p    =      ∑                  (                                                            λ                i                xe2x80x2                            -                              N                0                                                    λ              i              xe2x80x2                                ⁢                      (                                          v                i                                  xe2x80x2                  ⁢                                      xe2x80x83                                    ⁢                  h                                            ·                              X                xe2x80x2                                      )                          )            ⁢              Wv        i                  xe2x80x2          ⁢                      xe2x80x83                    ⁢          h                    
where N0 is a positive real number representing additive noise.
The additive noise can be made equal to the smallest of the eigenvalues xcexixe2x80x2.
Each eigenvalue of a subset of said eigenvalues xcexlxe2x80x2 having a contribution less than a predetermined threshold can be forced to the value of said additive noise.
This reduces complexity commensurately.
In a second variant of the method, the estimate of the covariance takes the form of a matrix R and said weighted estimate is established as follows:
Xp=(AtA+N0Rxe2x88x921)xe2x88x921At.S
where A is the measurement matrix associated with the training sequence and N0 is a positive real number representing the additive noise.
Whatever solution is adopted, when the instantaneous impulse response X has been estimated, the additive noise is advantageously obtained in the following manner:
estimating the instantaneous noise: N=Sxe2x88x92A.X,
normalizing the energy of this estimate of the instantaneous noise.
Also, said normalization is preferably followed by an averaging step.
If the above solution is not adopted in the second variant, the method can include a step of orthonormalizing the matrix R by means of a transformation matrix W to obtain a new matrix Rxe2x80x2, the weighted estimate then taking the following new form:
Xp=W(I+N0Rxe2x80x2xe2x88x921)xe2x88x921Axe2x80x2t.S
where the matrix Axe2x80x2 is equal to product of the transformation matrix W and said measurement matrix A.
The expression (I+N0Rxe2x80x2xe2x88x921)xe2x88x921 is advantageously calculated by means of the matrix inversion lemma.